An active tooth surface design methodology for face-hobbed hypoid gears based on measuring coordinates

An active tooth surface design methodology is proposed for face-hobbed hypoid gears based on fitting the measuring coordinates of real tooth surface that includes the flank deviations caused by machine errors and the deformation of heat treatment. Firstly, non-uniform rational B-spline (NURBS) is used as a tool to fit the discrete measuring coordinates of gear and pinion, then real tooth surface equations are obtained. Secondly, the pinion auxiliary tooth surface that is in line contact with the gear real tooth surface and has a parabolic transmission error (TE) is obtained by using the gear as a virtual cutter to generate the pinion under a predesigned motion function, then the pinion target tooth surface is obtained by modifying the pinion auxiliary tooth surface along the contact line with a predesigned contact pattern (CP). Thirdly, an optimization model is proposed to solve the adjustments of pinion machining parameters, this model is solved by using sequence quadratic program (SQP). The feasibility of this methodology is demonstrated by using a numerical example of a Klingelnberg-Oerlikon's Spirac hypoid gear set; the results are in line with the preconditions. This proposed methodology provides a new approach for meshing performances control of face-hobbed hypoid gears in the phase of trial-manufacture.